(x+2)(x+3)+(x-4)(x+5)=

Solution for (x+2)(x+3)+(x-4)(x+5)= equation:

Simplifying
(x + 2)(x + 3) + (x + -4)(x + 5) = 0

Reorder the terms:
(2 + x)(x + 3) + (x + -4)(x + 5) = 0

Reorder the terms:
(2 + x)(3 + x) + (x + -4)(x + 5) = 0

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + (x + -4)(x + 5) = 0
((3 * 2 + x * 2) + x(3 + x)) + (x + -4)(x + 5) = 0
((6 + 2x) + x(3 + x)) + (x + -4)(x + 5) = 0
(6 + 2x + (3 * x + x * x)) + (x + -4)(x + 5) = 0
(6 + 2x + (3x + x2)) + (x + -4)(x + 5) = 0

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + (x + -4)(x + 5) = 0

Reorder the terms:
6 + 5x + x2 + (-4 + x)(x + 5) = 0

Reorder the terms:
6 + 5x + x2 + (-4 + x)(5 + x) = 0

Multiply (-4 + x) * (5 + x)
6 + 5x + x2 + (-4(5 + x) + x(5 + x)) = 0
6 + 5x + x2 + ((5 * -4 + x * -4) + x(5 + x)) = 0
6 + 5x + x2 + ((-20 + -4x) + x(5 + x)) = 0
6 + 5x + x2 + (-20 + -4x + (5 * x + x * x)) = 0
6 + 5x + x2 + (-20 + -4x + (5x + x2)) = 0

Combine like terms: -4x + 5x = 1x
6 + 5x + x2 + (-20 + 1x + x2) = 0

Reorder the terms:
6 + -20 + 5x + 1x + x2 + x2 = 0

Combine like terms: 6 + -20 = -14
-14 + 5x + 1x + x2 + x2 = 0

Combine like terms: 5x + 1x = 6x
-14 + 6x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-14 + 6x + 2x2 = 0

Solving
-14 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + 3x + x2 = 0

Solving
-7 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 3x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x + x2 = 0 + 7
3x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
3x + x2 = 7

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + 3x + x2 = 9.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
x + 1.5 = 3.041381265

Simplifying
x + 1.5 = 3.041381265

Reorder the terms:
1.5 + x = 3.041381265

Solving
1.5 + x = 3.041381265

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.041381265 + -1.5
x = 3.041381265 + -1.5

Combine like terms: 3.041381265 + -1.5 = 1.541381265
x = 1.541381265

Simplifying
x = 1.541381265

Subproblem 2
x + 1.5 = -3.041381265

Simplifying
x + 1.5 = -3.041381265

Reorder the terms:
1.5 + x = -3.041381265

Solving
1.5 + x = -3.041381265

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.041381265 + -1.5
x = -3.041381265 + -1.5

Combine like terms: -3.041381265 + -1.5 = -4.541381265
x = -4.541381265

Simplifying
x = -4.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.541381265, -4.541381265}
Solution
x = {1.541381265, -4.541381265}